Faces Refuse to Merge - Merging Objects Faces between two Joined Objects
While in Edit Mode for the object which contains the problem face you want to be rid of, go to the Select menu at the top of the 3D View, then find Select All by Trait, and choose Non-Manifold. Only non-manifold geometry will be selected. Then you can press x to bring up the delete menu, and choose Faces, which will get rid of only the faces which were earlier selected as non-manifold. You might alternatively consider choosing the Loose Geometry option under the Select All by Trait menu. I mention this alternative because I find that the Non-manifold option does not always appear in the list, depending on the nature of the object's current topology.